The invention relates generally to a positioning technique in which a target device's location is estimated on the basis of observations on the target device's wireless communication environment. FIG. 1 schematically illustrates an example of such a positioning technique. A target device T communicates via base stations BS via a radio interface RI. In this example, the communication is assumed to be radio communication. The target device T observes signal values at the radio interface RI. The observation set OS is applied to a probabilistic model PM that models the target device's wireless communication environment and produces a location estimate LE.
A practical example of the target device is a data processing device communicating in a wireless local-area network (WLAN) or a cellular radio network. The data processing device may be a general-purpose laptop or palmtop computer or a communication device, or it may be a dedicated test or measurement apparatus such as a hospital instrument connected to the WLAN. A signal value, as used herein, is a measurable and location-dependent quantity of a fixed transmitter's signal. For example, signal strength and bit error rate/ratio are examples or measurable and location-dependent quantities. An example of a positioning technique that is based on a probabilistic model of a device's radio environment is disclosed in U.S. Pat. No. 6,112,095 to Mati Wax et al.
A problem underlying the invention is related to the fact that such a probabilistic model works best when it is dense. This means that the distance between sample points should not be too high. A sample point is a point of the probabilistic model. In an ideal case, the distance between sample points is equal to the desired resolution of the probabilistic model, which means that the sample point that best matches the target device's observations is considered to be the target device's location. A problem is that obtaining a large number of sample points by physical calibration is time-consuming and expensive. This process is difficult to perform automatically. As a result, some sample points should be determined by deriving them from known calibrated locations, for example, by interpolation. But, surprisingly, such interpolation is far from trivial.
FIG. 2 illustrates a problem related to interpolation of signal values. The independent variable x represents a measurable signal value, such as signal strength. The dependent variable P(x) is the probability of that signal value. FIG. 2 shows probability distributions 21 and 22 for two locations Q1 and Q2, respectively. To keep FIG. 2 simple, the probability distributions 21 and 22 are assumed to be non-overlapping. The signal values for location Q1 are concentrated near value X1 and the signal values for location Q2 are concentrated near value X2.
Assume that we wish to predict signal values at a sample point that is between the locations Q1 and Q2. For example, we might wish to insert into the probabilistic model a sample point that is between two locations for which actual measurements or simulation results are available. An intuitive way to create such a new sample point is to combine the probability distributions 21 and 22 for locations Q1 and Q2. Curve 23, that is shown in a bold dash line, represents such a combined (and normalized) probability distribution. But such a combined probability distribution 23 does not predict signal values between two locations, at least not very well. This is because the combined probability distribution 23 has nonzero probability values only for signal values that have nonzero probabilities in either of the original probability distributions 21 and 22. Accordingly, the intuitive way to combine the probability distributions 21 and 22 produces a result which is counter-intuitive and apparently false. In FIG. 2, the signal value is quantified to discrete values, but the result is the same if x is treated as a continuous variable.
Thus a problem is how to create a sample point based on interpolation of two or more known locations. This problem can be generalized as follows: how to construct a probabilistic model that models a target device's wireless environment for positioning the target device, such that the probabilistic model can be constructed on the basis of diverse information. The model may be based on calibration measurements, simulations or theoretical calculations or any combination thereof. The model should be generic enough to be able to make best possible use of any information available.